Question

In right triangle ABC, ∠B is the right angle and m∠C = 30°. If AC = 10, what is AB?
A. 5
B. 5v3
C. 20
D. 5v3/3

Answer 1

AC is the hypotenuse = 10

AB is side opposite to <C

<C = 30°, <B = 90°

by 30°-60°-90° theorem

side opposite to 30° is equal to half of hypotenuse

therefore,

AB = 1/2 × AC

AB = 1/2 × 10

AB = 5

therefore, option number A. 5

hope it will help you

Answer 2

The answer is A) 5

Step-by-step explanation:

Given: a right triangle ABC, right-angles at B

Also, the measure of angle C is 30 degrees, and AC = 10

To find: AB

Solution:

We can use the relation of sine in a right triangle and solve the given question as follows:

$sin 30\° = \frac{perpendicular}{Hypotenuse}$

$sin 30\° = \frac{AB}{AC}$

Substituting the values, of sin 30 = 1/2 and AC = 10, we get

$\frac{1}{2} = \frac{AB}{10}$

On cross multiplication, we obtain

$AB = \frac{10}{2}$

AB = 5

Hence, option A is correct.